Method for calculating natural vibration frequency of steel-concrete composite beam under common boundary condition

Abstract

The invention discloses a method for calculating the natural vibration frequency of a steel-concrete composite beam under common boundary conditions, and relates to the technical field of high-speed railway bridge construction. The method comprises the steps that material parameters and the cross sectional area of the steel-concrete composite beam are obtained; calculating a dimensionless coefficient according to material parameters and section parameters of the steel-concrete composite beam; according to the dimensionless coefficient, the first frequency reduction coefficient, the bending resistance combination connection coefficient, the second frequency reduction coefficient and the third frequency reduction coefficient; and calculating the natural vibration frequency of the single-span steel-concrete composite beam under the common boundary condition according to the three frequency reduction coefficient calculation expressions. According to the method, the shear deformation influence is considered, the frequency approximate value of the single-span steel-concrete composite beam under any boundary condition can be calculated, the calculation precision is high, and the method is also suitable for other partially-interacted composite beams formed by connecting two different materials through flexible shear connectors.

Description

Technical Field

[0001] The present application relates to the technical field of high - speed railway bridge construction, and particularly relates to a calculation method for the natural vibration frequency of steel - concrete composite beams under common boundary conditions. Background Art

[0002] A steel - concrete composite beam is a structural form that can be stressed integrally, composed of a concrete slab and a steel beam combined through shear connectors, and is often used in the fields of high - speed railway bridge construction and building structures. However, under the action of reciprocating vehicle loads or seismic excitations, the composite beam often exhibits complex dynamic responses. Therefore, it is particularly important to analyze the dynamic performance of steel - concrete composite beams.

[0003] In the prior art, the design code for steel - concrete composite beams is mainly based on the stiffness reduction method. This method is applicable to the static calculation of composite beams. However, there are significant limitations in the dynamic response analysis, and the influence of shear deformation is not considered. For composite beams with a small aspect ratio and the analysis of high - order frequencies, ignoring shear deformation will cause a large error in the calculation results; the precise dynamic method has errors in the calculation of long elements, and the high - order mode analysis calculation is limited, resulting in insufficient calculation accuracy of the natural vibration frequency under dynamic response to meet the actual engineering requirements.

[0004] Therefore, there is an urgent need for a calculation method to improve the calculation accuracy of the natural vibration frequency of composite beams under dynamic response and enhance its application value in actual engineering. Summary of the Invention

[0005] Based on this, in view of the above - mentioned technical problems, it is necessary to provide a calculation method for the natural vibration frequency of steel - concrete composite beams under common boundary conditions.

[0006] The present specification adopts the following technical solutions: The present specification provides a calculation method for the natural vibration frequency of steel - concrete composite beams under common boundary conditions, including: Obtaining the material parameters and cross - sectional area of the steel - concrete composite beam; Calculating dimensionless coefficients according to the material parameters and cross - sectional area of the steel - concrete composite beam; the dimensionless coefficients include: shear key stiffness combination coefficient, sub - beam section stiffness ratio coefficient, shear - bending stiffness ratio combination coefficient, and height - span ratio coefficient; Calculating a first frequency reduction coefficient and a flexural combination connection coefficient generated by interface relative slip and shear deformation according to the dimensionless coefficients; Calculating a second frequency reduction coefficient according to the flexural combination connection coefficient and the sub - beam section stiffness ratio coefficient; calculating a third frequency reduction coefficient according to the measured ratio of the span to the height of the steel - concrete composite beam and the sub - beam section stiffness ratio coefficient; Calculate the natural vibration frequency of a single-span steel-concrete composite beam under common boundary conditions according to the first frequency reduction coefficient, the second frequency reduction coefficient, and the third frequency reduction coefficient.

[0007] Preferably, the material parameters of the steel-concrete composite beam include: shear key stiffness, elastic modulus, shear modulus, flexural moment of inertia, intrinsic modal length of the composite beam, distance from the neutral axis of the concrete slab to the steel-concrete interface, and distance from the neutral axis of the steel beam to the steel-concrete interface.

[0008] Preferably, calculate the combined coefficient of the shear key stiffness based on the material parameters and cross-section parameters of the steel-concrete composite beam, specifically including: Calculate the combined coefficient of the shear key stiffness according to the shear key stiffness, the distance from the neutral axis of the concrete slab to the steel-concrete interface, the distance from the neutral axis of the steel beam to the steel-concrete interface, the elastic modulus, the shear modulus, the flexural moment of inertia, and the cross-sectional area. The formula is: ; In the formula, α , β and γ are the combined coefficients of the shear key stiffness, K is the shear key stiffness, E is the elastic modulus, G is the shear modulus, A c is the cross-sectional area of the concrete slab, A s is the cross-sectional area of the steel beam, I c is the flexural moment of inertia of the concrete slab, I s is the flexural moment of inertia of the steel beam, h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface, h = h c +h s .

[0009] Preferably, calculate the sub-beam cross-section stiffness ratio coefficient and the shear-bending stiffness ratio combined coefficient based on the material parameters and cross-section parameters of the steel-concrete composite beam, specifically including: Calculate the sub-beam cross-section stiffness ratio coefficient according to the cross-sectional area, the distance from the neutral axis of the concrete slab to the steel-concrete interface, the distance from the neutral axis of the steel beam to the steel-concrete interface, the elastic modulus, and the flexural moment of inertia. The formula is: ; In the formula, χ is the sub-beam cross-section stiffness ratio coefficient, A is the total cross-sectional area of the concrete slab and the steel beam, A = A s +A c, I is the total flexural moment of inertia of the concrete slab and the steel beam, I = I s +I c ; Calculate the shear-bending stiffness ratio combination coefficient according to the shear modulus, cross-sectional area, distance from the neutral axis of the concrete slab to the steel-concrete interface, distance from the neutral axis of the steel beam to the steel-concrete interface, elastic modulus, and flexural moment of inertia. The formula is: ; In the formula, δ, κ and μ are the shear-bending stiffness ratio combination coefficients, G is the shear modulus, I F = I + Ah 2 , I = I s +I c , A = A s + A c .

[0010] Preferably, for the material parameters of the steel-concrete composite beam, calculate the height-span ratio coefficient, specifically including: Calculate the height-span ratio coefficient according to the natural modal length sum of the composite beam, the distance from the neutral axis of the concrete slab to the steel-concrete interface, and the distance from the neutral axis of the steel beam to the steel-concrete interface. The formula is: ; In the formula, is the height-span ratio coefficient, L eqn is the natural modal length of the composite beam corresponding to the n th vibration mode frequency, h= h c +h s , h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface.

[0011] Preferably, the calculation formula for the first frequency reduction coefficient is: ; In the formula, η n is the first frequency reduction coefficient, α , β and γ are the combination coefficients of the shear key stiffness;χ is the stiffness ratio coefficient of the secondary beam section; δ, κ and μ is the combined coefficient of shear-bending stiffness ratio; ς is the coefficient related to the ratio of height to span.

[0012] Preferably, the calculation formula for the flexural combination connection coefficient is: ; In the formula, α * is the flexural combination connection coefficient.

[0013] Preferably, the second frequency reduction coefficient is calculated based on the flexural combination connection coefficient and the stiffness ratio coefficient of the secondary beam section, specifically including: When the vibration mode order n ≤ 5, the second frequency reduction coefficient is calculated based on the flexural combination connection coefficient and the stiffness ratio coefficient of the secondary beam section. The calculation formula for the second frequency reduction coefficient ψ 1 is: ; When n > 5, ψ 1 = 1.

[0014] Preferably, the calculation formula for the third frequency reduction coefficient is: ; In the formula, ψ 2 is the third frequency reduction coefficient, L is the span of the composite beam, H is the beam height.

[0015] Preferably, the calculation formula for the natural vibration frequency of a simply supported single-span steel-concrete composite beam under common boundary conditions is: ; In the formula, is commonly used the natural vibration frequency of the simply supported single-span steel-concrete composite beam under the boundary conditions, η n is the first frequency reduction coefficient, ψ 1 is the second frequency reduction coefficient, ψ 2 is the third frequency reduction coefficient, I F = I + Ah 2 , where A is the total cross-sectional area of the concrete slab and the steel beam, A = A s +A c , I is the total flexural moment of inertia of the concrete slab and the steel beam, I = I s +I c ,I c is the flexural moment of inertia of the concrete slab, I s is the flexural moment of inertia of the steel beam, m is the mass of the composite beam per unit length, A c is the cross-sectional area of the concrete slab, A s is the cross-sectional area of the steel beam, L eqn is the vibration mode frequency, and is the corresponding eigenmode length of the composite beam at the n -th order, h = h c +h s , where h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface.

[0016] The above at least one technical solution adopted in this specification can achieve the following beneficial effects: A calculation method for the natural vibration frequency of a steel-concrete composite beam under common boundary conditions provided by the present invention is based on the Shear composite beam theory, considering the influence of shear deformation. By using the material parameters and cross-sectional areas of the steel-concrete composite beam, three frequency reduction coefficients are calculated respectively, and based on the three frequency reduction coefficients, the natural vibration frequency of the steel-concrete composite beam under common boundary conditions is calculated. This calculation method is applicable to calculating the approximate value of the natural vibration frequency of a single-span steel-concrete composite beam under any boundary conditions, has high calculation accuracy, and is also applicable to other partially interacting composite beams composed of two different materials connected by flexible shear connectors. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the present application and form a part of the present application. The schematic embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings: Figure 1 is a schematic flow chart of a calculation method for the natural vibration frequency of a steel-concrete composite beam under common boundary conditions provided by this specification; Figure 2 is a schematic diagram of a composite beam of a calculation method for the natural vibration frequency of a steel-concrete composite beam under common boundary conditions provided by this specification; Figure 3 is a structural diagram of a test beam of a steel-concrete composite beam under a uniform load provided by this specification. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments of this specification and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the specification without creative efforts belong to the scope of protection of this application.

[0019] The technical solutions provided by each embodiment of this application will be described in detail below in conjunction with the drawings.

[0020] Figure 1 It is a schematic flow chart of a calculation method for the natural vibration frequency of a steel-concrete composite beam under a common boundary condition in this specification, specifically including the following steps: S101: Obtain the material parameters and cross-sectional area of the steel-concrete composite beam.

[0021] Optionally, for the structural schematic diagram of the steel-concrete composite beam, see Figure 2 , the material parameters of the steel-concrete composite beam include: shear key stiffness, elastic modulus, shear modulus, bending moment of inertia, natural mode length of the composite beam, distance from the neutral axis of the concrete slab to the steel-concrete interface, and distance from the neutral axis of the steel beam to the steel-concrete interface.

[0022] S102: Calculate dimensionless coefficients according to the material parameters and cross-sectional parameters of the steel-concrete composite beam; the dimensionless coefficients include: combined coefficient of shear key stiffness, stiffness ratio coefficient of sub-beam cross-section, shear-bending stiffness ratio coefficient, and height-span ratio coefficient.

[0023] Optionally, to calculate the combined coefficient of shear key stiffness according to the material parameters and cross-sectional parameters of the steel-concrete composite beam, it specifically includes: Calculate the combined coefficient of shear key stiffness according to the shear key stiffness, distance from the neutral axis of the concrete slab to the steel-concrete interface, distance from the neutral axis of the steel beam to the steel-concrete interface, elastic modulus, shear modulus, bending moment of inertia, and cross-sectional area. The formula is: ; In the formula, α , β and γ are the combined coefficients of shear key stiffness, K is the shear key stiffness, E is the elastic modulus, G is the shear modulus, A c is the cross-sectional area of the concrete slab, A s is the cross-sectional area of the steel beam, I c is the bending moment of inertia of the concrete slab, I s is the bending moment of inertia of the steel beam, h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, hs Denotes the distance from the neutral axis of the steel beam to the steel-concrete interface, h = h c +h s .

[0024] Optionally, according to the material parameters and cross-section parameters of the steel-concrete composite beam, calculate the sub-beam section stiffness ratio coefficient and the shear-bending stiffness ratio combination coefficient, specifically including: Calculate the sub-beam section stiffness ratio coefficient according to the cross-sectional area, the distance from the neutral axis of the concrete slab to the steel-concrete interface, the distance from the neutral axis of the steel beam to the steel-concrete interface, the elastic modulus, and the flexural moment of inertia. The formula is: ; In the formula, χ is the sub-beam section stiffness ratio coefficient, A is the total cross-sectional area, and I is the total flexural moment of inertia; Optionally, calculate the shear-bending stiffness ratio combination coefficient according to the shear modulus, cross-sectional area, the distance from the neutral axis of the concrete slab to the steel-concrete interface, the distance from the neutral axis of the steel beam to the steel-concrete interface, the elastic modulus, and the flexural moment of inertia. The formula is: ; In the formula, δ, κ, μ is the shear-bending stiffness ratio combination coefficient, G is the shear modulus, and I F =I + Ah 2 , I = I s + I c .

[0025] Among them, ; .

[0026] Optionally, calculate the height-span ratio coefficient according to the material parameters of the steel-concrete composite beam, specifically including: Calculate the height-span ratio coefficient according to the natural modal length of the composite beam, the distance from the neutral axis of the concrete slab to the steel-concrete interface, and the distance from the neutral axis of the steel beam to the steel-concrete interface. The formula is: ; In the formula, is the height-span ratio coefficient, L eqn is the natural modal length of the composite beam corresponding to the n th vibration mode frequency, h= h c +h s , h c denotes the distance from the neutral axis of the concrete slab to the steel-concrete interface, hs It represents the distance from the neutral axis of the steel beam to the steel-concrete interface.

[0027] S103: Calculate the first frequency reduction coefficient and the flexural combination connection coefficient generated by the relative slip and shear deformation of the interface according to the dimensionless coefficient.

[0028] Optionally, the calculation formula for the first frequency reduction coefficient is: ; In the formula, η n is the first frequency reduction coefficient, α , β and γ are the combined coefficients of the shear key stiffness; χ is the sub-beam section stiffness ratio coefficient; δ, κ and μ are the combined coefficients of the shear-bending stiffness ratio; ς is the coefficient related to the ratio of height to span.

[0029] Optionally, the calculation formula for the flexural combination connection coefficient is: ; In the formula, α * is the flexural combination connection coefficient.

[0030] S104: Calculate the second frequency reduction coefficient according to the flexural combination connection coefficient and the sub-beam section stiffness ratio coefficient; calculate the third frequency reduction coefficient according to the ratio of the span to the height of the measured steel-concrete composite beam and the sub-beam section stiffness ratio coefficient.

[0031] Optionally, calculating the second frequency reduction coefficient according to the flexural combination connection coefficient and the sub-beam section stiffness ratio coefficient specifically includes: When the vibration mode order n ≤ 5, calculate the second frequency reduction coefficient according to the flexural combination connection coefficient and the sub-beam section stiffness ratio coefficient, and the second frequency reduction coefficient ψ 1's calculation formula is: ; When n > 5, ψ 1 = 1.

[0032] Optionally, the calculation formula for the third frequency reduction coefficient is: ; In the formula, ψ 2 is the third frequency reduction coefficient, L is the span of the composite beam, H is the beam height.

[0033] S105: Calculate the natural vibration frequency of a single-span steel-concrete composite beam under common boundary conditions according to the first frequency reduction coefficient, the second frequency reduction coefficient, and the third frequency reduction coefficient.

[0034] Optionally, the calculation formula for the natural vibration frequency of a single-span steel-concrete composite beam under common boundary conditions is: ; In the formula, is commonly used The natural vibration frequency of a single-span steel-concrete composite beam under boundary conditions, η n is the first frequency reduction coefficient, ψ 1 is the second frequency reduction coefficient, ψ 2 is the third frequency reduction coefficient, I F = I + Ah 2 , where A is the total cross-sectional area of the concrete slab and the steel beam, A = A s +A c , I is the total flexural moment of inertia of the concrete slab and the steel beam, I = I s +I c , I c is the flexural moment of inertia of the concrete slab, I s is the flexural moment of inertia of the steel beam. m is the mass of the composite beam per unit length, A c is the cross-sectional area of the concrete slab, A s is the cross-sectional area of the steel beam, L eqn is the vibration mode frequency, and is the corresponding eigenmode length of the composite beam at the n th order, h = h c +h s , where h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface.

[0035] Among them, ; Specifically, since this approximate expression is derived by large-scale calculation and mathematical induction based on a simply supported steel-concrete composite beam at both ends, the error of the simply supported beam at both ends in the example is 0.

[0036] Specifically, the cross-section of the test beam adopted in this embodiment is generally in the shape of an I-beam, and its structural diagram is shown in Figure 3 ; the upper concrete slab is rectangular with a cross-sectional size of 1700 mm × 300 mm; the lower part is an I-shaped steel beam with a cross-sectional size of 550 mm × 450 mm × 28 mm; the total length of the test beam is 8.5 m, and the calculated span is 8.0 m; the diameter of the shear studs is 22 mm, and the stiffness is K = 1574 MPa, arranged in 4 rows horizontally, with a total of 168 shear studs. The structural dimensions and the arrangement of the shear studs are shown in Figure 3 . The material parameters are: E c = 30 GPa, G c = 12.5 GPa, ρ c = 2600 kg / m 3 ; E s = 206 GPa, G s = 79.231 GPa, ρ c = 7850 kg / m 3 . The structural parameters are: A c = 0.51 m 2 , I c = 0.003825 m 4 ; A s = 0.0406 m 2 , I s = 0.002495 m 4 , and the calculation results are shown in Table 1,

[0037] Table 1 Comparative Analysis of Approximate Solutions for the Frequencies of Simply Supported Composite Beams under Common Boundary Conditions

[0038] Note: The error is the error of the calculation result of the present invention relative to the exact solution.

[0039] The exact solution is the frequency value calculated by using the dynamic stiffness matrix method. The calculation result of the present invention is basically consistent with the exact solution, and the maximum relative error is only 3.4%, verifying the engineering applicability of the approximate expression for the frequency of the simply supported composite beam proposed by the present invention.

[0040] ] When applying the calculation method for the natural vibration frequency of a steel-concrete composite beam under a common boundary condition provided in this specification, it is not necessary to Figure 1 ​The steps shown are executed in sequence, and the specific execution sequence of each step can be determined as needed. This specification does not impose any restrictions on this.

[0041] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

Claims

1. A calculation method for the natural vibration frequency of a steel-concrete composite beam under common boundary conditions, characterized in that, Including: Obtain the material parameters and cross-sectional areas of the steel-concrete composite beam; Calculate the dimensionless coefficients based on the material parameters and cross-sectional areas of the steel-concrete composite beam; The dimensionless coefficients include: shear key stiffness combination coefficient, sub-beam section stiffness ratio coefficient, shear-bending stiffness ratio combination coefficient, and span-depth ratio coefficient; Calculate the first frequency reduction coefficient and flexural combination connection coefficient caused by interface relative slip and shear deformation according to the dimensionless coefficients; Calculate the second frequency reduction coefficient according to the flexural combination connection coefficient and sub-beam section stiffness ratio coefficient; calculate the third frequency reduction coefficient according to the measured ratio of the span to the height of the steel-concrete composite beam and the sub-beam section stiffness ratio coefficient; Calculate the natural vibration frequency of a single-span steel-concrete composite beam under common boundary conditions according to the first frequency reduction coefficient, the second frequency reduction coefficient, and the third frequency reduction coefficient.

2. The calculation method of the natural vibration frequency of a steel-concrete composite beam under common boundary conditions as described in claim 1, wherein, The material parameters of the steel-concrete composite beam include: shear key stiffness, elastic modulus, shear modulus, flexural moment of inertia, natural modal length of the composite beam, distance from the neutral axis of the concrete slab to the steel-concrete interface, and distance from the neutral axis of the steel beam to the steel-concrete interface.

3. The calculation method of the natural vibration frequency of a steel-concrete composite beam under a common boundary condition as described in claim 2, wherein, Calculate the combination coefficient of the shear key stiffness according to the material parameters and section parameters of the steel-concrete composite beam, specifically including: Calculate the combination coefficient of the shear key stiffness according to the shear key stiffness, distance from the neutral axis of the concrete slab to the steel-concrete interface, distance from the neutral axis of the steel beam to the steel-concrete interface, elastic modulus, shear modulus, flexural moment of inertia, and cross-sectional area. The formula is: ； In the formula, α , β and γ are the shear key stiffness combination coefficients, K is the shear key stiffness, E is the elastic modulus, G is the shear modulus, A c is the cross-sectional area of the concrete slab, A s is the cross-sectional area of the steel beam, I c is the flexural moment of inertia of the concrete slab, I s is the flexural moment of inertia of the steel beam, h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface, h = h c +h s .

4. The calculation method of the natural vibration frequency of a steel-concrete composite beam under common boundary conditions as described in claim 3, characterized in that, Calculate the sub-beam section stiffness ratio coefficient and the shear-bending stiffness ratio combination coefficient according to the material parameters and section parameters of the steel-concrete composite beam, specifically including: Calculate the sub-beam section stiffness ratio coefficient according to the cross-sectional area, distance from the neutral axis of the concrete slab to the steel-concrete interface, distance from the neutral axis of the steel beam to the steel-concrete interface, elastic modulus, and flexural moment of inertia. The formula is: ； In the formula, χ is the stiffness ratio coefficient of the secondary beam section, A is the total cross-sectional area of the concrete slab and the steel beam, A = A s +A c , I is the total flexural moment of inertia of the concrete slab and the steel beam, I = I s +I c ; Calculate the shear-bending stiffness ratio combination coefficient according to the shear modulus, cross-sectional area, distance from the neutral axis of the concrete slab to the steel-concrete interface, distance from the neutral axis of the steel beam to the steel-concrete interface, elastic modulus, and flexural moment of inertia. The formula is: ； In the formula, δ, κ and μ are the combined coefficients of shear-bending stiffness ratios, G is the shear modulus, I F = I + Ah 2 , I = I s +I c , A = A s +A c .

5. The calculation method of the natural vibration frequency of a steel-concrete composite beam under common boundary conditions as described in claim 2, characterized in that, Calculate the span-depth ratio coefficient according to the material parameters of the steel-concrete composite beam, specifically including: Calculate the span-depth ratio coefficient according to the natural modal length of the composite beam, distance from the neutral axis of the concrete slab to the steel-concrete interface, and distance from the neutral axis of the steel beam to the steel-concrete interface. The formula is: ； In the formula, is the high-span ratio coefficient, L eqn is the eigenmode length of the composite beam corresponding to the n -th order of the vibration mode frequency, h = h c + h s , h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface.

6. The calculation method of the natural vibration frequency of a steel-concrete composite beam under a common boundary condition according to claim 1, characterized in that, The calculation formula for the first frequency reduction coefficient is: ； In the formula, η n is the first frequency reduction coefficient, α , β and γ are the combined coefficients of the shear key stiffness; χ is the sub-beam section stiffness ratio coefficient; δ, κ and μ are the combined coefficients of the shear-bending stiffness ratio; ς is the coefficient related to the height-span ratio.

7. The calculation method of the natural vibration frequency of a steel-concrete composite beam under common boundary conditions as described in claim 6, characterized in that The calculation formula for the flexural combination connection coefficient is: ； In the formula, α * is the bending resistance combined connection coefficient.

8. The calculation method of the natural vibration frequency of a steel-concrete composite beam under common boundary conditions according to claim 6, characterized in that Calculate the second frequency reduction coefficient according to the flexural combination connection coefficient and the sub-beam section stiffness ratio coefficient, specifically including: When the vibration mode order n ≤ 5, calculate the second frequency reduction coefficient according to the flexural combination connection coefficient and the sub-beam section stiffness ratio coefficient. The calculation formula for the second frequency reduction coefficient ψ 1 is as follows: ； When n > 5, ψ 1 = 1.

9. The calculation method of the natural vibration frequency of a steel-concrete composite beam under common boundary conditions according to claim 6, characterized in that The calculation formula for the third frequency reduction coefficient is: ； In the formula, ψ 2 is the third frequency reduction coefficient, L is the span of the composite beam, H is the beam height.

10. The calculation method of the natural vibration frequency of a steel-concrete composite beam under a common boundary condition according to claim 1, characterized in that, The calculation formula for the natural vibration frequency of a single-span steel-concrete composite beam under common boundary conditions is: ； In the formula, For common The natural vibration frequency of a single-span steel-concrete composite beam under boundary conditions, η n is the first frequency reduction coefficient, ψ 1 is the second frequency reduction coefficient, ψ 2 is the third frequency reduction coefficient, I F = I + Ah 2 , where A is the total cross-sectional area of the concrete slab and the steel beam, A = A s +A c , I is the total flexural moment of inertia of the concrete slab and the steel beam, I = I s +I c , I c is the flexural moment of inertia of the concrete slab, I s is the flexural moment of inertia of the steel beam, m is the mass of the composite beam per unit length, A c is the cross-sectional area of the concrete slab, A s is the cross-sectional area of the steel beam, L eqn is the vibration mode frequency, and is the corresponding eigenmode length of the composite beam at the n th order, h = h c +h s , where, h c represents the distance from the neutral axis of the concrete slab to the steel-concrete interface, h s represents the distance from the neutral axis of the steel beam to the steel-concrete interface.

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